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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
If $g\left( x \right) = \mathop \smallint \limits_0^x \cos 4t\;dt$ then $g\left( {x + \pi } \right) = $
  • A
    $\frac{{g\left( x \right)}}{{g\left( \pi \right)}}$
  • B
    $g\left( x \right) + g\left( \pi \right)$
  • C
    $g\left( x \right) - g\left( \pi \right)$
  • ✓
    $(b) $ and $(c)$ both
✓

Answer

Correct option: D.
$(b) $ and $(c)$ both
d
$(a,d):g(x) = \int\limits_0^x {\cos 4tdt} $

$\Rightarrow g(x)=\left[\frac{\sin 4 t}{4}\right]_{0}^{x}=\frac{\sin 4 x}{4}$

$\Rightarrow g(x+\pi)=\frac{\sin 4(x+\pi)}{4}=\frac{\sin 4 x}{4}$

$\Rightarrow g(\pi)=0 \Rightarrow g(x+\pi)=g(x)+g(\pi) \text { or } g(x)-g(\pi)$

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